Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space

We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3...

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Bibliographic Details
Published inarXiv.org
Main Authors de Medeiros, Paul, Figueroa-O'Farrill, José, Méndez-Escobar, Elena
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.06.2008
Subjects
Algebra
Asymptotic properties
Lie groups
Linear algebra
Mathematics - Representation Theory
Physics - High Energy Physics - Theory
Quantum theory
Topological manifolds
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Summary:We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3-algebras. We establish a one-to-one correspondence between one branch of the moduli space and compact riemannian symmetric spaces. We analyse the asymptotic behaviour of the moduli space and identify a large class of models with moduli branches exhibiting the desired N^{3/2} behaviour.
Bibliography:EMPG-08-06
ISSN:2331-8422
DOI:10.48550/arxiv.0805.4363